Auction software often allows bidders (for example, suppliers) to specify multiple attributes associated with their bids, such as quality, terms and conditions, etc. Consequently, bidders can differentiate themselves by factors other than price.
Weighting factors enable buyers to rate the relative importance of attributes that may be associated with bids. A buyer can specify weighting factors for each attribute using a sliding scale, in which the user can choose from various options such as “do not care”, “important”, “more important”, “very important”, and “most important”.
There also exists software for performing “Request for Quotes” (RFQ). Some software permits complex configuration and bill-of-material relationships. Suppliers can specify quotes having ranges of attributes, and price variations for terms and conditions. In some cases, a buyer can post a RFQ, and the software automatically (i) searches supplier's rules (predefined and stored in a database), (ii) calculates a best offer for each supplier, and (iii) ranks all offers according to criteria that are most important to a buyer.
In some existing RFQ software, buyers (that is, users) can specify the weighting factors of each attribute explicitly. However, these softwares demand a thorough knowledge/perception about the attributes from a user. On the other hand, rest of the software accept input from a user about the order (partial or full) on the items or bids and extract the weighting factors (utilities) of the attributes from the specified order.
In software that accepts an ordered list (full or partial) of items/bids from a user, the utility function of the item/bid is expressed as a parametric function of the attributes. There exist a number of investigations concerning techniques for representing the utility function of the bids/items having multiple attributes and subsequent techniques for the parametric model fitting on the ordinal data sets (that is, ordered set of items). In general, such an approach may be classified as belonging to multi-attribute utility theory (MAUT).
In multi-attribute utility theory (MAUT), parametric utility functions can be classified according to different levels of complexity. Types of parametric utility function include multilinear, multiplicative, and additive models. Solutions to the problem of evaluating attributes are proposed for additive models only, the utilities for individual attributes are considered to be independent. For additive utility functions, evaluation of the utility function, and subsequent ranking of the objects, is performed by assessing the weights of the attributes by formulating the problem as a linear programming task.
There are two primary limitations associated with the existing tools described above.
First, users' preference structures are represented by what is essentially a linear additive utility function, namely a weighted sum of utility functions for individual attributes. For example, if attributes associated with a bid are price and quality, then a relevant utility function for the buyer, U(price, quality), is defined as U(price, quality)=w1×U(price)+w2×U(quality). In this expression, U(price) and U(quality) are respectively the buyer's individual utility functions for price and quality.
Second, individual attribute utility functions are assumed a priori. In the example above, U(price) and U(quality) are assumed to be known, and the buyer effectively specifies weights w1 and w2 by indicating the relative importance of the respective attributes on a sliding scale, such as that described above.
In view of the above observations, a need clearly exists for representing a user's preferences when selecting between competing alternatives.